Does 'smutna' change based on the gender of the person you're speaking to?
Yes - mezczyzna jest smutny, kobieta jest smutna, dziecko jest smutne.
(please excuse me for the missing accents)
I understand that "a sad child" would be "smutne dziecko", but if you were asking this question to a child would you use smutny/smutna?
You'd use the child's gender. If you were not sure about it, then you have a problem ;) 'smutne' is an option, I guess, but even a child could consider it weird.
Thanks Marek, that's what I thought :)
Czemu jesteś smutna? Can it be correct? What is the difference between czemu and dlaczego?
It's perfectly fine, it's an accepted answer.
There isn't any real difference, really. But some people can consider 'czemu' a bit worse, a bit colloquial version, claiming that it's a Russicism.
Why do we not use the instrumental form of smutny here following jesteś?
Noun phrases need Instrumental, but standalone adjectives just take Nominative. Compare "Dlaczego jesteś smutną kobietą?" and "Dlaczego jesteś smutna?".
Thank-you for your explanstion.